Let's simplify the expression step by step:

(81x - 306) * 32 = 412864 - 412288

First, let's expand the left side of the equation:

2592x - 9792 = 412864 - 412288

Now, combine like terms on the right side of the equation:

2592x - 9792 = 576

Now, isolate the variable x by adding 9792 to both sides of the equation:

2592x = 10368

Finally, divide both sides by 2592 to solve for x:

x = 4

Therefore, the solution to the equation is x = 4.